Multi-travelling waves for the nonlinear Klein-Gordon equation

Abstract

For the nonlinear Klein-Gordon equation in R 1 + d \mathbb {R}^{1+d} , we prove the existence of multi-solitary waves made of any number N N of decoupled bound states. This extends the work of Côte and Muñoz (Forum Math. Sigma 2 (2014)) which was restricted to ground states, as were most previous similar results for other nonlinear dispersive and wave models.